Viability of perturbative expansion for quantum field theories on neurons

arXiv:2508.03810v4 Announce Type: replace-cross Abstract: Neural Network (NN) architectures that break statistical independence of parameters have been proposed as a new approach for simulating local quantum field theories (QFTs). In the infinite neuron number limit, single-layer NNs can exactly reproduce QFT results. This paper examines the viability of this architecture for perturbative calculations of local QFTs for finite neuron number N using scalar phi^4 theory in d Euclidean dimensions as an example. We find that the renormalized O(1/N) corrections to two- and four-point correlators yield perturbative series which are sensitive to the ultraviolet cut-off and therefore have a weak convergence. We propose a modification to the architecture to improve this convergence and discuss constraints on the parameters of the theory and the scaling of N which allow us to extract accurate field theory results.

Source: arXiv cs.LG | 2026-05-18